KVPY Sample Paper KVPY Stream-SX Model Paper-30

If \[z=\frac{1}{2}(i\sqrt{3}-1)\], then the value of \[(z-{{z}^{2}}+2{{z}^{3}})(2-z+{{z}^{2}})\] is

A) 3

B) 7

C) \[-1\]

D) 5

Correct Answer: B

Solution :

\[z=\omega \Rightarrow (z-{{z}^{2}}+2{{z}^{3}})(2-z+{{z}^{2}})\]

\[=(\omega -{{\omega }^{2}}+2)(2-\omega +{{\omega }^{2}})\]

\[={{\left| 2-\omega +{{\omega }^{2}} \right|}^{2}}={{\left| 2-i\sqrt{3} \right|}^{2}}=7\]